SCV vs. AV

[esand...@gmail.com]

Is it possible for the single-choice (plurality) voting winner to have less Bayesian Regret than the approval winner?

If so, how? (Working on a rebuttal/reply to someone)

[Warren D Smith]

--BR is not really defined/intended for 1 election, it is defined in terms of
zillions of elections, average performance.

But certainly it is possible for plurality to outperform approval on one
election.

[esand...@gmail.com]

Curious, any idea what the probability is that PV will outperform AV for any given election? Or is that too vague of a question to even model?

[Warren D Smith]

On 2/2/16, esand...@gmail.com <esand...@gmail.com> wrote:

> Curious, any idea what the probability is that PV will outperform AV for any
> given election? Or is that too vague of a question to even model?

it could be made a more precise question, in a specific
model of voter behaviors, utilities, etc.
At which point it then would have an answer.

For example, if the approval voters' behavior was "plurality voting"
then their BR would be the same...

[Warren D Smith]

An example where plurality outperforms approval is, V voters,
N candidates, each has slightly less than V/N plurality
voters, except for one who has slightly more then V/N
(the winner). All N totally unrelated, hence no vote-splitting
or anything, and (let us suppose) the winner really did
deserve it in the sense he delivered the most utility...
*except* let us postulate this winner suffered having a near-clone
who got especially few votes.

Meanwhile, with approval, if each voter approves two,
that plur winner and his near-clone both get approved by less than 2V/N,
while everybody else gets about 2V/N.

---

Another example: sometimes approval, or socre cvoting, or whatever,
can deliver a suboptimal-utility winner.
But plurality if that winner happens to be aided by some fortunate vote-split,
can in the right situation make him win.

I.e. design the vote-split to make the best guy win,
even though in more advanced voting systems than plurality, which
get rid of the vote-splitting problem. he would not be able to win.

I.e. vote-splitting is usually a problem, but sometimes it can help.
Depends on the election.

--
Warren D. Smith
http://RangeVoting.org <-- add your endorsement (by clicking
"endorse" as 1st step)

[esand...@gmail.com]

How can SV deliver a sub-optimal utility winner? With 'strategic' voters?

[Warren D Smith]

also with honest voters.

On 2/2/16, esand...@gmail.com <esand...@gmail.com> wrote:

> How can SV deliver a sub-optimal utility winner? With 'strategic' voters?
>

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[Warren D Smith]

the point is, scores in score voting, are not the same thing as,
(and cannot be the same thing as, even if some
voter tries to make be) utilities.

hence score voting has nonzero BR.

[esand...@gmail.com]

How are 'honest' scores not indicative of underlying utilities?

[Clay Shentrup]

Because of normalization. And even if you didn't normalize, you wouldn't exactly know if your 4 was my 4. We do don't have a hedonimeter.

[esand...@gmail.com]

I see, thanks Clay and Warren!

[esand...@gmail.com]

One more thing--curious: Why have "Magic Best Winner" on the BR graph at all? Why not just shift everything over and replace it with the 'sincere' SV Winner, since the Magic Best Winner is impossible to determine anyway...?

[Jameson Quinn]

Best winner is not impossible to determine in the simulation, though it is in practice. It is not theoretically impossible for some non-score voting system under some assumptions to do better than honest score, so it's better to leave that space in there just in case.

2016-02-05 19:02 GMT-05:00 <esand...@gmail.com>:

One more thing--curious: Why have "Magic Best Winner" on the BR graph at all? Why not just shift everything over and replace it with the 'sincere' SV Winner, since the Magic Best Winner is impossible to determine anyway...?

[Clay Shentrup]

On Friday, February 5, 2016 at 4:02:17 PM UTC-8, esand...@gmail.com wrote:

One more thing--curious: Why have "Magic Best Winner" on the BR graph at all? Why not just shift everything over and replace it with the 'sincere' SV Winner, since the Magic Best Winner is impossible to determine anyway...?

It's a benchmark. Without it, you wouldn't have anything to compare the best system against. It would appear to be perfect, which is wrong.